Multiplication Tips and Tricks

There are a number of tips and tricks you can use that may help you with your multiplication. Different tricks help different people, so some of these may help you a lot, while others may not. Just try them out to see what works for you. 

Draw a Picture 

One of the simplest ways to understand multiplication is to draw a picture. 

Example: 

5 x 3 = ? 

 
Now you can just count up the dots to discover there are 15 total dots: 5 x 3 = 15. 

Use Multiples to Find the Answer 

Let's say you can't remember what 5 x 7 is, but you can remember that 5 x 5 = 25. Now you can just keep on adding 5's to 25: 25 + 5 = 30, 30 + 5 = 35, therefore 5 x 7 = 35. 

You can learn a lot and work on your times tables by counting in multiples. Try it for the number 4: 4, 8, 16, 20, 24, 28, 32, …. 

When Multiplying by the number....

• 2 - Remember that the answer will always be an even number. If your answer isn't even, then you need to try it again.
• 5 - The answer will always end in a 0 or a 5
• 10 - You just have to put a zero behind the other number. With 100 put two zeros.
• 11 - When multiplying 11 by numbers less than 10, you can just write the number twice for the answer. For example, 5 x 11 = 55, 8 x11 = 88

Break Apart the Number 

Some numbers are easy to break apart and then add the two results. This is pretty much what we do when we do long multiplication, but you can do it on smaller problems if it makes them easier to solve. 

Example: 

1) 14 x 12 = ? 

You may not have memorized 14 x 12, but you should know 7 x 12 if you learned the times table so you can do the following: 

(2 x 7 x 12) = 2 x 84 = 84 + 84 = 168 

2) 42 x 6 = ? 

In this case we will take advantage of 10s multiplying. We don't know what 42 x 6 is off the top of our head, but we do know 4 x 6 and 2 x 6, we can use these numbers to solve the problem: 

42 x 6 = (10 x 4 x 6) + (2 x 6) = (10 x 24) + 12 = 240 + 12 = 252 

Long Multiplication 

If you are having trouble with long multiplication, one idea is to circle the numbers you have already used. This way you won't accidentally use them again. 

Example: 

 
Go to our longmultiplication page for more on this subject. 

Fun Trick when Multiplying Numbers by 9 

This works when multiplying numbers up to 10 by the number 9. 

1) Hold your hands out in front of you with your fingers straight
2) Now, for whatever number you are multiplying 9 by, lower that finger. For example, if it is 9 x 4, lower the fourth finger from the right.
3) Now look at your fingers. If it was 9 x 4, you have three fingers still up to the right of the finger you lowered and six fingers on the left. This is actually the answer! 9 x 4 = 36.
4) Try this for other numbers and see that it works. It even works for 1 and 10 because if it's 1x9 you have 09, which is the same as 9. If your last finger is down for 9 x 10 you have 9 and 0 fingers up. That's 90! 

Long Multiplication

What is long multiplication? 

Long multiplication is a method used to solve multiplication problems with large numbers. One thing that can really help you in long multiplication is if you know the multiplication table by heart. This will speed up your work and make it more accurate. 

First Step 

The first step in long multiplication is to write down the numbers on top of each other. You align the numbers on the right. Don't worry about the decimal points when lining up the numbers; just write them down and line up the right-most number. 

Examples: 

469 x 32 87.2 x 19.5 113.05 x 47

Second Step 

Now we are going to start multiplying. We'll use the numbers from the first example above: 469 x 32. We begin with the ones place in the bottom number. This is the 2 in 32. We multiply 2x469 and write it down under the line. 
 

Adding a Zero for the Tens Space 

Now we need to multiply by the next number to the left of the 2. This is the 3 in 32. Because the 3 is in the tens place we need to hold the tens place by placing a zero in the 1's place before we start multiplying. 
 

Finish multiplying 

Multiply the 3 by the top number (469) and write this number next to the zero. 


If there were more numbers we would add more rows and continue to add more zeros. For example, if there were a 4 in the hundreds spot (i.e. the number on the bottom was 432) we would add two zeros in the next row and then multiply 469 by 4. 

Third Step 

After we have multiplied all the numbers on the bottom, we add up the rows of numbers to get the answer. In this case there are two rows, but there would be more if the number we were multiplying by on the bottom (the 32) had more digits. 
 

Another Long Multiplication Example 

Below is an example long multiplication problem where the added zeros are shown in red and the carry numbers for each step are shown in blue. 
 

Multiplication Basics

What is multiplication? 

Multiplication is when you take one number and add it together a number of times. 

Example: 

5 multiplied by 4 = 5 + 5 + 5 + 5 = 20 

We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times". 

More examples:

• 7 x 3 = 7 + 7 + 7 = 21
• 2 x 1 = 2
• 3 x 6 = 3 + 3 + 3 + 3 + 3 + 3 = 18

Signs for Multiplication 

There are a few different signs that people use to indicate multiplication. The most common is the "x" sign, but sometimes people use a "*" sign or other symbols. Here are some ways to indicate 5 multiplied by 4.

• 5 x 4
• 5 * 4
• 5 times 4

Sometimes when people use variables in multiplication they will just put the variables next to each other to indicate multiplication. Here are a few examples:

• ab = a x b
• (a +1)(b + 1) = (a +1) x (b + 1)

Factors and Products 

Sometimes when teachers talk about multiplication they will use the terms factors and products. 

Factors are the numbers you are multiplying together. Products are the answers. 

(factor) x (factor) = product 

Multiplying by Zero and One 

Zero and one are two special cases when multiplying. 

When multiplying by 0, the answer is always 0. 

Examples:

• 1 x 0 = 0
• 7676 x 0 = 0
• 0 x 12 = 0
• 0 x b = 0

When multiplying by 1, the answer is always the same as the number multiplied by 1. 

Examples:

• 1 x 12 = 12
• 7654 x 1 = 7654
• 1 x 0 = 0
• 1 x b = b

Order Doesn't Matter 

An important rule to remember with multiplication is that the order you multiply numbers doesn't matter. You can multiply them in any order you want and the answer will be the same. This can help sometimes when you get stuck on a problem. Just try it the other way. 

Examples:

• 5 x 4 = 4 + 4 + 4 + 4 + 4 = 20
• 4 x 5 = 5 + 5 + 5 + 5 = 20

• 3 x 2 = 2 + 2 + 2 = 6
• 2 x 3 = 3 + 3 = 6

• 4 x 1 = 1 + 1 + 1 +1 = 4
• 1 x 4 = 4 = 4

Multiplication Table 

Once you learn the basics of multiplication, you will want to learn the multiplication table, also called the times table. This table includes all of the possible multiplications between the numbers 1 to 12. That is all the way from 1 x 1 to 12 x 12. 

It may sound like a lot of useless work to memorize this table, but it will help you a LOT later in school. You will be able to solve harder problems faster and easier if you know these numbers by heart. 

Here is the table: